and it is smooth whenever \((d,\chi )\)  are coprime.
For \(\gamma =[0,1,1)\) , corresponding to a D2-brane wrapped on a curve \(C\)  in the linear system
\(|H|\) , one has \(\mathcal {M}_\infty (\gamma )={P}^2\) . The Gieseker index, defined in the same way as
in (REF ), turns out to be completely independent of \(\chi \)  [1]}, and
related to the refined Gopakumar-Vafa invariants
\(N_{j_L,j_R}^d\)  [2]}, [3]} via
\(\Omega _\infty ( [0,d,\chi ) )= \sum _{j_L, j_R} (-1)^{2j_L+2j_R} \chi _{j_L}(y) \chi _{j_R}(y) N_{j_L,j_R}^d\) 
